Why were the Sadducees most concerned about Peter's preaching about Christ being alive?
The Sadducees denied any resurrection from the dead, believing people lived and died like animals. Peter’s preaching that Christ was alive and could yet return as King directly contradicted their doctrine, so they were grieved and confronted him for teaching what flew in the face of their belief.
Les explains that the Sadducees were the group most concerned about Peter’s preaching because they did not believe in resurrection from the dead. Their doctrine was that you lived like an animal and died like an animal. Peter, however, taught the people and preached through Jesus the resurrection from the dead, and that Christ was alive and yet able to come and be their King. This directly contradicted the Sadducees’ doctrine, so they came at Peter, grieved that he would dare teach something that flew in the face of their belief that there is no such thing as someone coming back from the dead.